![]() Zhou Q, Shao X, Jiang P, Gao Z, Wang C, Shu L (2016) An active learning metamodeling approach by sequentially exploiting difference information from variable-fidelity models. Kleijnen J P (2009) Kriging metamodeling in simulation: a review. Jiang P, Wang J, Zhou Q, Zhang X (2015) An enhanced analytical target cascading and Kriging model combined approach for multidisciplinary design optimization. Comput Model Eng Sci 22(2):97Įddy D C, Krishnamurty S, Grosse I R, Wileden J C, Lewis K E (2015) A predictive modelling-based material selection method for sustainable product design. Jiang C, Han X (2007) A new uncertain optimization method based on intervals and an approximation management model. The result reveals that the proposed approach provides more accurate metamodel at the same simulation cost, which is very important in metamodel-based engineering design problems.Ĭrombecq K, Laermans E, Dhaene T (2011) Efficient space-filling and non-collapsing sequential design strategies for simulation-based modeling. As a demonstration, the proposed approach is compared to other three sampling methods using several numerical cases and the modeling of the aerodynamic coefficient for a three-dimensional aircraft. By calculating the weight of the area and prediction error for each triangle region using the entropy method and TOPSIS, the degree of dispersion of sample points and local errors of metamodel are taken into consideration to make a trade-off between global exploration and local exploitation during the sequential sampling process. The area of each partitioned triangle is used to indicate the degree of dispersion of sample points, and the prediction error of Kriging metamodel at each triangle’s centroid is used to represent the local error of each triangle region. In the proposed KMDT, Delaunay triangulation is employed to partition the design space according to current sample points. This paper proposes an adaptive sampling strategy for Kriging metamodel based on Delaunay triangulation and TOPSIS (KMDT). Sampling method plays an important role in the constructing of metamodels. If they had very good outcomes, mostly positive, then they could also pause the observations ahead of time and save money rather than wait for the outcome when putting out all observations at the same time.Metamodels have been widely used in engineering design and optimization. If the number of negatives get large at the beginning of the observations, then the company could ban the treatment immediately to avoid future cost. Rather than putting out large numbers of observations at the same time and have them all failed at the end, observing sequentially often save time and money for the company. If a pharmaceutical company want to release a new treatment, how many people should they observe to ensure that the new treatment is valid. Sequential sampling is also widely used in treatment design. Instead of reading all of them, I could apply the sequential sampling method, each time I read a review, then I update my decision score for the restaurant and stop reading when the score reaches a point where I am sure of going or not. So how many of them should I read before I make my decision. There are forty review of the restaurant on the first page, some are short and some are lengthy. For example, I want to dine out at a fancy restaurant and go on Yelp to check the review for the restaurant. ![]() Observing sequentially is essential here.Īfter reading the paper, I found this application could be used restaurant selection. With the new belief about X_i, he can make decision between X_i and m by selecting the larger value or he could choose to take another observation and get more information about the alternative. The calculation for posterior distribution is based on Bayes’ Theorem. With the signals, he can calculate the posterior distribution of the unknown option, updating his belief for the new option. After each observation, he gets a signal Y for the alternative. Before selecting an alternative to implement, he/she can choose to sequentially sample one or more of the k different options to get evidence for the unknown means. He also has the choice to implement a know option whose expected reward is a known value m. For example, someone wants to implement one out of k alternatives whole rewards X_i are random with a particular prior distribution such as the normal distribution or beta distribution. The basic problem is The Sampling Selection Problem. The paper stated several different kind of sequential sampling problem. Bayes’ Theorem is also widely used in sequential sampling. Bayes’ Theorem stated how a subjective degree of belief should rationally change to account for evidence. In class, we discussed about they Bayes’ Theorem.
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